How do I separately apply color correction to a model and video clip?
OK, so here is what I would do:
I would strongly suggest that you render your model and put it on top of your image in 2D by simple image/videocomposite. Render out an exr or png sequence and then re-import that in Blender and use an alpha-over node in the compositor (you can also use any video editing software that way)
Then you can just put your image through any CC nodes and process it before merging.
I would also suggest using EEVEE, since you don't have any detail that relies on caustics. Should turn those 40min into 40s.
And as final tip: If you are using motion blur or depth of field, leave the plane in the background, but turn off camera visibility. This way it will already blend into the blurred areas saving you a lot of fine-tuning.